Abstract

This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. The efficiency of the proposed method is checked out in two 2D optimization problems using a full potential model coupled with a boundary layer model. The first one corresponds to an internal flow problem and the second one corresponds to an external flow problem. The work presented here can be considered as a continuation of previous work (Bugeda and Oñate, Int. J. Numer. Methods Fluids, 20, 915–924 (1995)). In that paper, the sensitivity analysis corresponding to both an incompressible potential flow and a Euler flow were derived together with a strategy for the adaptive remeshing. In the present paper, the sensitivity analysis is derived for a full potential flow coupled with a boundary layer model, and a new error estimator is employed.

Abstract

Abstract

Nature has evolved structural materials along millions of years of incremental changes to fulfil functional requirements of very different situations. Let´s take as an example the sharks, one of the best adapted species for swimming across the oceans, and their smooth skin that is composed of millions of small scales (denticles), with complex geometries formed by sharp spines and micro-grooves aligned with flow direction, varying in size and shape at different locations of the sharkskin. The purpose of this microstructure is to reduce the viscous drag produced by the water when it adheres to the hull forming the fluid boundary layer, which can stick out the added mass to the weight of the fish and increase dramatically its peak speed. Inspired by this natural solution, we have started the design of a bioinspired new material, to be incorporated to the hull wet surface, reducing the viscous drag and increasing the velocity and the efficiency (less fuel consumption) of the ship. In this way, it will be easier to control the green effect gas emissions while sailing. We present the development of this new bioinspired, hybrid material with scales obtained by additive manufacturing using polymeric materials. To control the orientation of the denticles respect to flow direction, the scales have been mounted on a substrate of hydrogel, who interact with the fluid field of pressures to adapt the angle of the moving scales as the velocity increases. No mechanical devices are needed, as the hydrogel act as a nonlinear spring accommodating the movements of the scales. CFD code helps in the development of the most efficient shape and coating design. A water channel has been developed to measure the actual forces acting on the surface of coated panels.

Abstract

The vertex-centered edge-based reconstruction (EBR) schemes for solving Eulertype equations are originally developed for tetrahedral unstructured meshes and imply the usage of quasi-one-dimensional straight-line reconstructions to calculate the flux. However, on the hybrid unstructured meshes with layers of highly anisotropic prismatic cells that are commonly used in simulations of turbulent flows with boundary layers, the straight-line reconstructions may lead to strongly irregular stencils, which cause both larger approximation errors and computational instabilities. To improve the accuracy and stability characteristics of EBR schemes on such meshes, we propose to use the curvilinear reconstructions for the flux computation. In this paper, we describe the principles and algorithms of constructing curvilinear reconstructions on the structured and semi-structured prismatic meshes. The modified EBR schemes are tested on the well-known NACA 0012 airfoil validation case for both two-dimensional and three-dimensional formulations, and the obtained numerical results are discussed in detail.